Why are Republicans so much stronger/Democrats weaker at the state level?

[Beezer]

It's really quite simple I'd say. The state level electorate looks different from the national one (particularly in presidential election cycles). Republican core voters (i.e. older whites) will always turn out, no matter what election we are talking about. Democratic core voters (i.e. younger voters and minorities) have a far poorer turnout record when there's a big name missing atop the ballot.